Optimal error estimation for H(curl)-conforming
p-interpolation in two dimensions
Alexei Bespalov and Norbert Heuer
SIAM J. Numer. Anal. 47 (5), 3977-3989, 2009.
In this paper we prove an optimal error estimate for
the H(curl)-conforming projection based p-interpolation operator
introduced in [L. Demkowicz and I. Babuska, p interpolation error
estimates for edge finite elements of variable order in two dimensions,
SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208]. This result is proved
on the reference element (either triangle or square) K
for regular vector fields in Hr(curl,K)
with arbitrary r>0.
The formulation of the result in the H(div)-conforming
setting, which is relevant for the analysis of high-order boundary element
approximations for Maxwell's equations, is provided as well.